A343683 Primes p1 such that the sum of 9 consecutive primes, p1+p2+p3+p4+p5+p6+p7+p8+p9, and the three sums (p1+p2+p3), (p4+p5+p6), (p7+p8+p9) are all prime numbers.

29, 83, 389, 1151, 2293, 2521, 2699, 2753, 4831, 7121, 9857, 12409, 13679, 24439, 25943, 36083, 43201, 47317, 49037, 49069, 49109, 51829, 51859, 53717, 61471, 64091, 68449, 70271, 77047, 87337, 87911, 90709, 111109, 113173, 114577, 117577, 117889, 118051, 128549, 134837, 149533, 172489

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..2500

Example

n=1, p1=29:
29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 = 401,
29 + 31 + 37 = 97, 41 + 43 + 47 = 131, 53 + 59 + 61 = 173, all primes.

Maple

R:= NULL: count:= 0:
P:= [seq(ithprime(i), i=1..9)]:
while count < 100 do
  P:= [P[2], P[3], P[4], P[5], P[6], P[7], P[8], P[9], nextprime(P[9])];
  if isprime(convert(P, `+`)) and isprime(P[1]+P[2]+P[3]) and isprime(P[4]+P[5]+P[6]) and isprime(P[7]+P[8]+P[9]) then
    R:= R, P[1]; count:= count+1;
  fi
od:
R; # Robert Israel, Jan 08 2026

Mathematica

Select[Prime@Range@10000, And@@PrimeQ[Flatten@{Total[s=NextPrime[#, 0~Range~8]], Total/@Partition[s, 3]}]&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)

Crossrefs

Cf. A082251 (primes that are the sum of 9 consecutive primes).

Sequence in context: A268612 A156784 A142592 * A255187 A273362 A195314

Adjacent sequences: A343680 A343681 A343682 * A343684 A343685 A343686

Keyword

nonn

Author

Zak Seidov, Apr 26 2021

Status

approved